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Properties

Label 625.2.h
Level $625$
Weight $2$
Character orbit 625.h
Rep. character $\chi_{625}(24,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $680$
Newform subspaces $2$
Sturm bound $125$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.h (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{50})\)
Newform subspaces: \( 2 \)
Sturm bound: \(125\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(625, [\chi])\).

Total New Old
Modular forms 1360 800 560
Cusp forms 1160 680 480
Eisenstein series 200 120 80

Trace form

\( 680 q + 20 q^{2} + 20 q^{3} + 20 q^{4} - 60 q^{6} + 25 q^{7} + 35 q^{8} + 20 q^{9} + O(q^{10}) \) \( 680 q + 20 q^{2} + 20 q^{3} + 20 q^{4} - 60 q^{6} + 25 q^{7} + 35 q^{8} + 20 q^{9} - 55 q^{11} - 60 q^{12} + 20 q^{13} - 10 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} + 10 q^{19} - 45 q^{21} + 25 q^{22} - 70 q^{23} - 15 q^{24} - 15 q^{26} + 20 q^{27} + 10 q^{28} + 10 q^{29} - 50 q^{31} + 25 q^{32} + 35 q^{33} - 30 q^{34} - 250 q^{36} + 55 q^{37} + 40 q^{38} - 45 q^{41} + 10 q^{42} + 25 q^{43} - 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 75 q^{49} - 5 q^{51} + 15 q^{52} + 15 q^{53} - 90 q^{54} - 145 q^{56} - 255 q^{58} - 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} - 65 q^{64} + 15 q^{66} - 105 q^{67} - 90 q^{69} - 125 q^{71} + 30 q^{72} + 40 q^{73} - 35 q^{74} + 5 q^{76} + 35 q^{77} - 100 q^{78} + 15 q^{81} - 175 q^{82} - 20 q^{83} - 185 q^{84} + 5 q^{87} + 5 q^{88} - 80 q^{89} - 145 q^{91} + 55 q^{92} - 275 q^{93} - 60 q^{94} + 135 q^{96} - 35 q^{97} + 15 q^{98} - 45 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(625, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
625.2.h.a 625.h 125.h $240$ $4.991$ None \(20\) \(20\) \(0\) \(25\) $\mathrm{SU}(2)[C_{50}]$
625.2.h.b 625.h 125.h $440$ $4.991$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{50}]$

Decomposition of \(S_{2}^{\mathrm{old}}(625, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(625, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)